Welcome
@jobhelp. I'll do my best to answer your questions.
1. "Push" is freight coming directly from DC and used to fill your empty areas of your store. "Pull" or "Pulls" is freight coming directly from your Backrooms and or if your store has an offsite. (Additional holding area for more freight). It is used to fill empty areas of your store as well only difference is it is being pulled by other people within your store to replenish an area.
2.When you get there at the beginning of your shift, it is best to check with your trainer or your Leader for that day as to what they might have you do specifically. (You might work the carts as you mentioned or assist the flow team with push).
3.Use what vehicle is easier for you whether it is a 3 tier, shopping cart or a flat. Most use a shopping cart because it's easier to maneuver. No you don't have to take everything at once.
4.Whatever you can't finish before your shift ends, bring back to the place where you originally picked it up from or ask your trainer or leader where to leave your unfinished push. If you can, label it with a note or if your store has them a label clip marked PULLS. Clips are usually green or yellow so ask your trainer or leader where they are in your store.
5. Yes baby items and shampoo/lotion are a part of Hardlines. Softllines consists of clothing and things to wear like hats and shades.
I hope I answered your questions as best and simply as I could. Good luck and don't forget to follow up with your trainer. That's what their SUPPOSED to do. Help!!